K-theory of line bundles and smooth varieties

We give a K-theoretic criterion for a quasi-projective variety to be smooth. If \mathbb{L} is a line bundle corresponding to an ample invertible sheaf on X, it suffices that K_q(X)\cong K_q(\mathbb{L}) for all q\le \dim (X)+1.

Saved in:
Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2018-10, Vol.146 (10), p.4139
Main Authors: C. Haesemeyer, C. Weibel
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We give a K-theoretic criterion for a quasi-projective variety to be smooth. If \mathbb{L} is a line bundle corresponding to an ample invertible sheaf on X, it suffices that K_q(X)\cong K_q(\mathbb{L}) for all q\le \dim (X)+1.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14112